Expressive Priors in Bayesian Neural Networks: Kernel Combinations and Periodic Functions
This work addresses the challenge of incorporating prior knowledge into BNNs for researchers and practitioners in machine learning, offering a principled approach that is incremental relative to existing Gaussian process methods.
The paper tackled the problem of designing expressive priors in Bayesian neural networks (BNNs) by deriving architectures that mirror kernel combinations from Gaussian processes, such as summing periodic and linear kernels to capture seasonal variation with trends. It demonstrated practical value through experiments in supervised and reinforcement learning, showing how BNNs can incorporate prior knowledge about functions.
A simple, flexible approach to creating expressive priors in Gaussian process (GP) models makes new kernels from a combination of basic kernels, e.g. summing a periodic and linear kernel can capture seasonal variation with a long term trend. Despite a well-studied link between GPs and Bayesian neural networks (BNNs), the BNN analogue of this has not yet been explored. This paper derives BNN architectures mirroring such kernel combinations. Furthermore, it shows how BNNs can produce periodic kernels, which are often useful in this context. These ideas provide a principled approach to designing BNNs that incorporate prior knowledge about a function. We showcase the practical value of these ideas with illustrative experiments in supervised and reinforcement learning settings.